Elastic properties of monolayer graphene with different chiralities.

Using molecular mechanics simulations we investigate the in-plane elastic properties of monolayer graphene with different chirality angles under both uniaxial stretching and free-standing indentation. The effect of the loading range is also considered: the tensile strain ranges of 2% and 5% are selected. Under uniaxial stretching, all of the elastic properties including the second-order elastic stiffness (E), the Poisson's ratio (ν) and the third-order elastic constant (c(m)) are essentially not sensitive to the graphene chirality angle. The values of E are essentially not sensitive to the tensile strain range (ε), while the values of c(m) slightly increase (numerically) with the decrease of ε. Under free-standing indentation, the values of E and c(m) determined are higher than those obtained from uniaxial stretching, and this difference significantly increases with the decrease of the tensile strain, especially for c(m). The difference between the in-plane stretching results and the indentation results arises mainly from the van der Waals (VDW) interaction between the indenter tip and the graphene, and the effect of the VDW interaction rapidly decreases with the tensile strain. The VDW effect is also not sensitive to the chirality angle. Therefore, a relatively large tensile strain is required (e.g. 5%) in order to obtain more accurate results from free-standing indentation.